Giovanni Leoni

Professor
Ph.D., University of Minnesota, Minneapolis

Office: Wean Hall 6128
Phone: (412) 268-2557
Fax: (412) 268-6380
E-mail: giovanni@andrew.cmu.edu

Research

My current research interests lie in calculus of variations, partial differential equations and geometric measure theory with special emphasis on applications to problems in continuum mechanics and in materials science.

Selected Publications

Books

1) Modern Methods in the Calculus of Variations: Lp Spaces, (in collaboration with I. Fonseca), Springer Monographs in Mathematics. Springer, New York, 2007.

2) Modern Methods in the Calculus of Variations: Sobolev Spaces, (in collaboration with I. Fonseca), in preparation, accepted for publication by Springer.

3) A First Course in Sobolev Spaces, Graduate Studies in Mathematics series, American Mathematical Society, Providence, RI, 2009.

Papers

1) On optimal regularity of free boundary problems and a conjecture of De Giorgi (in collaboration with H. Koch and M. Morini) Comm. Pure Appl. Math. 58 (2005), no. 8, 1051-1076;

2) Weak continuity and lower semicontinuity results for determinants (in collaboration with I. Fonseca and J. Malý Archive Rational Mech. Anal. 178 (2005), no. 3, 411-448;

3) Renormalized Energy and Forces on Dislocations (in collaboration with P. Cermelli) SIAM Journ. Math. Anal. 37 (2005), no. 4, 1131-1160;

4) Necessary and sufficient conditions for the chain rule in W^{1;1}_{loc}(R^N;R^d) and BV_{loc}(R^N;R^d) (in collaboration with M. Morini) J. Eur. Math. Soc. (JEMS) 9 (2007), no. 2, 219-252;

5) Equilibrium configurations of epitaxially strained crystalline films: existence and regularity results, in collaboration with I. Fonseca, N. Fusco and M. Morini) Arch. Rational Mech. Anal. 186 (2007) 477-537;

6) A higher order model for image restoration: the one dimensional case, in collaboration with G. Dal Maso, I. Fonseca, and M. Morini, to appear in SIAM Journ. Math. Anal.

7) Gradient theory for plasticity via homogenization of discrete dislocations, in collaboration with A. Garroni and M. Ponsiglione, to appear in J. Eur. Math. Soc. (JEMS).